%%%%%%%%%%%%%%%%%%%%%
%% Paul's Math Defs
%% Operators
\newcommand{\norm}[1]{\left\Vert#1\right\Vert}
\newcommand{\abs}[1]{\left\vert#1\right\vert}
\newcommand{\pd}[2]{{\frac{\partial #1}{\partial #2}}}

%% Matrix shortcuts
\newcommand{\bbm}{\begin{bmatrix}}
\newcommand{\ebm}{\end{bmatrix}}

%%%%%%%%%%%%%%%%%%%%%%%%%
%% UTIAS Notation
%%

% Basic bold for letters and symbols
\DeclareMathAlphabet{\mbf}{OT1}{ptm}{b}{n}
\newcommand{\mbs}[1]{{\boldsymbol{#1}}}

% helper bold symbols
\newcommand{\mbsbar}[1]{{\overline{\boldsymbol{#1}}}}
\newcommand{\mbshat}[1]{{\hat{\boldsymbol{#1}}}}
\newcommand{\mbsvec}[1]{{\underrightarrow{\boldsymbol{#1}}}}
\newcommand{\mbsdel}[1]{{\delta {\boldsymbol{#1}}}}
\newcommand{\mbsDel}[1]{{\delta {\boldsymbol{#1}}}}
\newcommand{\mbsdot}[1]{{\dot {\boldsymbol{#1}}}}
\newcommand{\mbsddot}[1]{{\ddot {\boldsymbol{#1}}}}
\newcommand{\mbc}[1]{{{\boldsymbol{\mathcal{#1}}}}}
\newcommand{\mbcbar}[1]{{\overline{\boldsymbol{\mathcal{#1}}}}}
\newcommand{\mbchat}[1]{{\hat{\boldsymbol{\mathcal{#1}}}}}
\newcommand{\mbcvec}[1]{{\underrightarrow{\boldsymbol{\mathcal{#1}}}}}
\newcommand{\mbcdel}[1]{{\delta {\boldsymbol{\mathcal{#1}}}}}
\newcommand{\mbcDel}[1]{{\delta {\boldsymbol{\mathcal{#1}}}}}
\newcommand{\mbcdot}[1]{{\dot {\boldsymbol{\mathcal{#1}}}}}
\newcommand{\mbcddot}[1]{{\ddot {\boldsymbol{\mathcal{#1}}}}}
\newcommand{\mbfbar}[1]{{\overline{\mbf{#1}}}}
\newcommand{\mbfhat}[1]{{\hat{\mbf{#1}}}}
\newcommand{\mbfvec}[1]{{\underrightarrow{\mbf{#1}}}}
\newcommand{\mbfdel}[1]{{\delta{\mbf{#1}}}}
\newcommand{\mbfDel}[1]{{\delta{\mbf{#1}}}}
\newcommand{\mbfdot}[1]{{\dot{\mbf{#1}}}}
\newcommand{\mbfddot}[1]{{\ddot{\mbf{#1}}}}

% A coordinate frame definintion
\newcommand{\cframe}[1]{{\smash{\underrightarrow{\mathcal{F}}_{#1}}}}

%new notation for homogeneous coordinates:
\DeclareMathAlphabet{\mathbfit}{OML}{cmm}{b}{it}
\newcommand{\homo}[1]{{\mathbfit{#1}}}
\newcommand{\mbfhbar}[1]{{\overline{\homo{#1}}}}
\newcommand{\mbfhhat}[1]{{\hat{\homo{#1}}}}
\newcommand{\mbfhdel}[1]{{\delta{\homo{#1}}}}
\newcommand{\mbfhdot}[1]{{\dot{\homo{#1}}}}
\newcommand{\mbfhddot}[1]{{\ddot{\homo{#1}}}}
\newcommand{\mbfh}[1]{{\homo{#1}}}

% Vectors
\renewcommand{\Vec}[1]{{\underrightarrow{#1}}}

% Operators
\newcommand{\argmax}{\operatornamewithlimits{argmax}}
\newcommand{\argmin}{\operatornamewithlimits{argmin}}

% Quaternions
\newcommand{\qc}[1]{{#1}^+}
\newcommand{\qo}[1]{{#1}^\oplus}
\newcommand{\qi}[1]{{#1}^{\scalebox{0.5}{$-1$}}}
\def\ep{\epsilon}
\def\la{\lambda}

\def\R{\mathbb R}


\newenvironment{notation}{\vspace{3mm}\begin{tabular}[t]{r @{\;\;\;:\;\;\;} p{.80\textwidth}}}{\end{tabular}\vspace{3mm}}
\newcommand{\nitem}[2]{\raggedleft $\displaystyle {#1}$ & #2\\}

